A square of paper is folded one or more times, a hole is punched or a corner is cut, and you must picture the sheet unfolded. No question from this topic appeared in the papers I could extract or recover, so this chapter is built entirely to the AAI pattern.
Every fold creates a crease that behaves exactly like a mirror line. Once that connection is made, this chapter becomes an extension of mirror images rather than a new topic.
When paper is folded, the crease becomes an axis of symmetry. Anything punched or cut through the folded layers appears twice in the unfolded sheet, reflected across that crease, exactly as in a mirror image question.
To predict the unfolded pattern, unfold the last fold made first, reflecting everything across that crease. Then unfold the next-to-last fold, reflecting the now-larger pattern across that crease, and so on until the paper is flat.
Always undo the folds in the reverse of the order they were made. Unfolding out of order scrambles the reflections and is the single biggest source of mistakes in this topic.
This is the simplest case and the foundation for every harder variant. A single fold plus a single punch always produces exactly two holes once unfolded, unless the punch happens to land exactly on the crease itself.
One fold doubles a single punch into two holes. Two folds double it again into four holes. The only exception is a punch placed exactly on a fold line, which does not get doubled by that particular fold, since it has nowhere to reflect to.
Ignore the shape of the paper and just count folds. Each one doubles whatever the punch count already is, so n folds give 2 to the power n holes, unless a punch sits exactly on a crease.
Most AAI-style questions use two folds, sometimes with two punches. Work through the folds one at a time rather than trying to picture the whole thing at once.
After the last fold, mark the punch position. Unfold the most recent crease and reflect the punch across it — now there are two marks. Unfold the next crease and reflect both marks across it — now there are four. Continue until flat.
Trying to reflect across two creases simultaneously is where most errors creep in. Unfold and reflect one crease fully, then move to the next.
A square sheet is folded in half vertically, then in half again horizontally, forming a smaller square one quarter the original size. A hole is punched near the folded corner that is not on either crease. How many holes appear when the sheet is fully unfolded, and roughly where?
Instead of a round punch, some questions cut a notch out of a folded edge or snip off a folded corner. The same reflection principle applies, but now a whole shape is mirrored, not just a point.
If a triangular notch is cut out of the folded edge itself, unfolding produces a shape that is symmetric about that edge — often a diamond or a larger triangle, twice the size, straddling where the fold used to be.
Deciding whether the cut touches the crease is the first thing to check in every fold-and-cut question, since it determines whether you get one combined shape or two separate mirrored ones.
Practice covering single and multiple folds, punches on and off the crease, and fold-and-cut questions, with blank squares printed for you to fold and sketch on. Print it, solve it, keep it.
Multiple choice questions, building in difficulty. Full solutions are in the downloadable PDF above.
Live classes cover every reasoning, aptitude, English and GK topic straight from the real question papers, with the shortcut for each question type drilled until it is automatic.